Use the graph of f in the figure to find the following values ...

Question

Use the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why.

l. $lim over x right arrow 2 of f of x$

Accepted Answer

Welcome back. Everyone refer to the graph of the function F FX to find a given limit if it exists. If the limit does not exist. Write DNE, we're looking for the limit of F FX as X approaches four. Here we have our graph of F FX. And for our answer choices A says the limit is four. B says it's five C says it's three and D says it does not exist. Now, how can we know if the limit exists? And if so what the limit is well given our function F FX, OK. We were trying to find the limit as X approaches for then the limit exists. OK. The limit, let me write that properly here. The limit exists if the limit of our function from the left hand side that is as X approaches for, from the left is equal to the limit as X approaches four from the right for F FX. In other words, we need to figure out what the limit is as it approaches from both sides. And if they are equal, that means the limit exists and is the value that they are approaching. So first, let's try to figure out what those values are from the left and the right. So when X equals four on our graph, OK, let me just put this dotted line to represent when X equals four here. OK. And then we know that that point would be right here, this point that I've shaded in black. Now, what do we notice first as it's approaching from the left? Well as our function is approaching X equals four from the left. OK. Then we notice that F FX is approaching five. OK. So the limit as X approaches four from the left of F FX is equal to five. Next, if we look at it from the right. OK. We look at our limit from the right. Notice that as X is approaching four from the right, sorry as our function is up as X is approaching four from the right, our function is approaching five as well. OK. So this tells us then that from the right hand side, the limit as X approaches four from the right of F FX is equal to five. Notice here that our left hand side, our left hand limit sorry is equal to our right hand limit. So that tells us then that the limit exists. OK. The limit exists. And furthermore, that limit as X approaches four of F of X is going to be equal to five. Therefore, when we look back at our answer choices, B is the correct answer. Thanks. A lot for watching everyone. I hope this video helped.

Use the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>

l. $lim over x right arrow 2 of f of x$

Key Concepts

Limits

Continuity

Existence of Limits

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